A procedure for the one-parametric linear complementarity problem

Abstract

We propose a principal pivoting method for solving the one-parametric linear complementarity problem where all the coefficients are linear functions of the parameter K and the matrix of the problem is sufficient for all values of the parameter in the interval under consideration. We increase k from to A subprogram using the least-index rule is developed for passing by the critical points at which the basis must be changed. The solution vector is a piecewise rational function of the parameter. It turns out that, under a restrictive assumption, the procedure is finite (if the problem becomes infeasible when increasing the parameter, the procedure must be terminated). We give some special cases in which the restrictive assumption holds. As a by-product, we obtain a new proof for the criss-cross method for the linear complementarity problem with a sufficient matrix. We also consider some applications of the procedure: parametric methods for the linear complementarity problem with a sufficient matrix, applicat...